Binary hypothesis testing; Bayes, minimax and Neyman-Pearson tests. Composite hypothesis testing.
Signal detection in discrete time: Models and detector structures. Coherent detection in independent noise. Detection in Gaussian noise. Detection of signals with random parameters. Detection of stochastic signals. Performance evaluation of signal detection procedures.
Bayesian parameter estimation; MMSE, MMAE and MAP estimates. Nonrandom parameter estimation. Exponential families. Completeness theorem. ML estimation. Information inequality. Asymptotic properties of MLEs.
Discrete time Kalman- Bucy filter. Linear estimation. Orthogonality principle. Wiener- Kolmogorov filtering – causal and noncausal filters.
Signal detection in continous time:Detection of deterministic signals in Gaussian noise. Coherent detection in white Gaussian noise.
1. H.V.Poor, “An Introduction to Signal Detection and Estimation (2/e) Springer”, 1994.
2. B.C.Levy, “Priciples of Signal Detection and Parameter Estimatio”n, Springer, 2008.
1. H.L.Vantrees, “Detection, Estimation and Modulation theory”, Part I, Wiley,1987.
2. M.D.Srinath & P.K.Rajasekaran, “Statistical Signal Processing with Applications”, Wiley, 1979.
3. J.C.Hancock & P.A. Wintz, “Signal Detection Theory”, Mc-Graw Hill, 1966.
Students are able to
CO1: summarize the fundamental concept on Statistical Decision Theory and Hypothesis Testing
CO2: summarize the various signal estimation techniques with additive noise
CO3: summarizer with Bayesian parameter estimation (minimum mean square error (MMSE), minimum mean absolute error (MMAE), maximum a-posterior probability (MAP) estimation methods).
CO4: compare optimal filtering, linear estimation, and Wiener/Kalman filtering.
CO5: construct Wiener and Kalman filters (time discrete) and state space models.
